The statistical analysis of all the fits are achieved by implementing a Markov Chain Monte-Carlo (MCMC) algorithm. More specifically, we used the MCMC algorithm implemented in XSPEC to create a chain of parameter values whose density gives the probability distribution for that parameter. For each individual spectrum fitting, two chains of 250000 steps are run with 20 walkers. The first \(10^4\)  steps of the running are discarded as burn-in phase. Convergence between these two chains is assessed by Gelman-Rubin diagnostic [1]}, which requires \(\left| {R-1} \right| < 0.01\) .
The analysis of the probability distributions derived from the MCMC chains is implemented using the corner package [2]}, to estimate the mean values and errors of model parameters.
